WO2001098751A1

WO2001098751A1 - Method for determining surface tension of a comminuted solid

Info

Publication number: WO2001098751A1
Application number: PCT/FR2001/001906
Authority: WO
Inventors: Gérard TERROM
Original assignee: It Concept
Priority date: 2000-06-20
Filing date: 2001-06-19
Publication date: 2001-12-27
Also published as: FR2810401B1; US20030164027A1; EP1301768A1; JP2004503741A; FR2810401A1

Abstract

The invention concerns a method for determining the surface tension of a comminuted solid based on different experimental measurements and different mathematical equations. Said method uses the principle of capillary rise of a probe liquid through a tube partly filled with the comminuted solid and closed on one side with a permeable membrane. The method consists in firstly allowing the liquid to rise freely in the tube, in producing a first counter-pressure on the tube, in allowing once more the free rising system, then in applying a second counter-pressure. Throughout the process the evolution of the liquid mass having risen in the tube is measured on a time basis. And based on different mathematical equations, the surface tension Ωs of the comminuted solid is calculated.

Description

PROCESS FOR DETERMINING THE SURFACE ENERGY OF A FINELY DIVIDED SOLID.

The present invention relates to a method for determining the surface energy of a finely divided solid, so as to better define its surface characteristics and properties.

More specifically, this process uses the combination of different experimental measurements with mathematical equations. The various chemical industries which use finely divided solids (also called powder) to prepare compositions, regularly face problems when dispersing the powder in a liquid, or when drying the powder which very easily tends to to agglomerate, or quite the contrary after being compressed, disintegrates with difficulty or then too easily.

Consequently, in order to resolve these drawbacks, it is necessary to seek to minimize the interfacial energy in order to improve the wetting or the stability of the solid-liquid dispersion compositions.

Also in order to be able to act better on the interfacial energy values, it is necessary to know them as precisely as possible.

In the prior methods known hitherto for determining the surface energy of powder, the principle of successive capillary rise of different liquids is used in a tube partially filled with the finely divided solid, the energy of which is sought to determine. area. Unlike liquid bodies, in this case, we cannot work by deformation of the surface. Thus the measurement of this energy can prove difficult to obtain precisely.

Kinetic monitoring of the capillary rise of a liquid rising in a tube (called probe liquid) in a porous medium to be studied (such as a powder) is one of the simplest methods to implement.

The kinetics of capillary rise is obtained by following the variation in mass of the tube filled with powder, over time.

Unfortunately, such methods require the use of several probe liquids, and a perfect knowledge of the geometric characteristics of the porous network of the powder column.

In addition, the direct transposition of the experimental surface energy measurement mechanisms, from a compact solid to a finely divided solid, in mathematical equations well known to those skilled in the art, such as the Washburn equation, poses many problems.

Indeed, the physical characteristics of the porous network of the divided solid must be perfectly defined in order to then be able to correctly calculate the surface energy of this solid.

Also, there remains the need to have a method for quickly and very easily determining the surface energy γ _s of a solid finely divided by the principle of capillary rise of a liquid in a tube filled with this solid. using a single probe liquid.

The subject of the invention is therefore a method for determining the surface energy γ _s of a finely divided solid from various experimental measurements and different mathematical equations consisting of:

- take a tube whose lower end is hermetically sealed by a liquid permeable membrane,

- to fill it to about 80% of its total volume with said divided solid,

- immerse the lower part closed by the membrane in a liquid, - allow the liquid to rise freely in the first phase in the tube,

- to measure the mass of the liquid mounted in the tube as a function of time by monitoring the change in mass of the remaining liquid, in order to obtain the slope 1 of the straight line described by the following equation (I): m ² = f (t) (equation I) characterized in that:

- in a second phase, when 10 to 20% of the total height of the powder is in contact with the liquid, a first pressure is applied to the upper part of the tube so as to stop the capillary rise of the liquid in the tube through the divided solid, and to measure the numerical value of the mass of liquid remaining after the rise of the liquid so as to deduce therefrom after mathematical calculation the mass of liquid mounted in the tube as soon as the assembly constituted by the pressure and the variation mass stabilized, then after applying the mathematical equation: ΔP = (A.Δγ) - (εpgh) (equation II) to obtain the numerical value of (A.Δγ) where

- A is the specific area of the finely divided solid (m ² / m ³ ), - Δγ = γ _s - Y _S is the difference between the surface energy of the solid (γ _s ) and the solid-liquid interfacial energy (γ _SL ),

- ε is the porosity of the divided solid - p is the density of the liquid (kg / m ³ )

- g is the acceleration of gravity (9.81)

- h is the height of the finely divided solid in the tube,

- ΔP is the pressure variation applied to the tube, to stop, in a third phase, the application of the first counter pressure so as to allow the liquid to rise freely in the tube until the divided solid is completely submerged in the liquid present in the tube, and to regularly measure the variation in the mass of liquid remaining, after the liquid has risen in the tube, as a function of time, to then deduce after mathematical calculation the total mass of the liquid mounted in the tube, and then obtain, after application of the mathematical equation (I), the slope 2, then the porosity ε according to the following equation (III):

volume of liquid at saturation ε - (equation III) volume of powder in the tube

Then by applying the mathematical equation (IV)

(ε-π-R ² ) ²

Ω _exp = x (A.Δγ) (equation IV) β

or

- Ω _exp (kg. M / s ² ) is equal to [1 / (2 xr _ιiq )] x slope 2 with r _ιig = p / η, η being the viscosity of the probe liquid in Pa. s,

- R is the internal radius of the tube

- ε is the porosity of the solid divided the numerical value of β, where β is the coefficient of tortuosity,

to apply, in a fourth step, to the upper part of the tube, a vacuum maintained constant for a period ranging from approximately 300 to 1000 seconds so as to measure the numerical value of the liquid mass remaining after the liquid has risen in the tube, to then deduce by mathematical calculation the kinetics of variation of the mass of liquid mounted in the tube, then the numerical value of the specific area A (m ² / m ³ ) of the powder in the tube, from 1 ' following Kozeny-Carman equation (V):

.DELTA.P

_A 2 _ x (equation V)

5.η .h.v (1-ε) or

- ΔP is the pressure variation applied to the tube, - η is the viscosity of the liquid,

- h is the height of powder in the tube,

- v is the rate of ascent of the liquid,

- ε is the porosity of the divided solid,

- And to apply again, in a fifth step, on the upper part of the tube, a second counter pressure kept constant for a period ranging from approximately 300 to 1000 seconds so as to calculate again the numerical value of the specific area A (m ² / m ³ ) as defined in step 4. The invention has the advantage of determining the surface energy γ _s of a powder in a simple, rapid, reliable and perfectly reproducible manner, and with only one probe liquid.

The subject of the invention is also a use of the method as defined above for determining the surface energy of finely divided solid entering into the chemical composition of solid-liquid dispersion, of paints, inks, adhesives, resins . Finally, a final object of the invention relates to the use of the method defined above for determining the surface energy of a finely divided, agglomerated solid.

The Washburn mathematical equation (Equation VI) describes a parabolic variation of the mass "m" of the liquid as a function of time "t", due to its capillary rise in the tube, according to: m ² = (2r ₂ .t ) (equation VI) where - (g): mass of liquid present in the tube,

- t (s): time,

- r _α : a parameter.

Obtaining capillary ascent kinetics makes it possible to evaluate the parameter r from the slope of the straight line m ² = f (t) -

T _x is defined by the following equation: r _x = r _sol . r _liq . Δγ

AT . fε .π. R ² ] ² with ≈ (eαuation VII)

* ground P ²

_F * - liq = (equation VIII) η

where A, ε, R, β, p, η have the same definitions as above.

Ω _exp is given by the following equation (IX) already cited:

1 Ω _{exp =} x slope 2

2 ^χ r _liq

and β by the following equation (X):

β = x (A.Δγ)

In the case of a porous column, the parameters ε, A and β make it possible to characterize the network formed in the finely divided solid.

The porosity value ε is easily accessible experimentally. Indeed, when the liquid soaks the entire tube partially filled with the powder having a height "h", the weight gain of the tube "m" gives directly, after mathematical calculation, the value of the tortuosity β.

On the other hand, A (interfacial area per unit of volume) and β (tortuosity coefficient) require additional experimental measurements.

These two parameters A and β are moreover easily determined according to the method of the invention, and this without having to use several probe liquids, or several mathematical operations with several unknown.

Preferably, the divided solid is chosen from mineral solids which may be in the finely divided state, such as organic or mineral polymers of synthetic origin such as, for example, polytetrafluoroethylene (PTFE) or polyethylene, or also from polymers organic or minerals of natural origin such as talc, glass, flour of various cereals or among the bacterial walls.

The liquid can be chosen from alkanes such as pentane, hexane, heptane, octane, nonane, decane, cyclohexane, hexadecane, cis-decaline, 1 'α-bromonaphthalene, diiodomethane, or among other organic compounds such as methanol, ethanol, methyl ethyl ketone, tetrahydrofuran (THF), ethylene glycol, glycerol, formamide, dimethyl sulfoxide, 1, 'water.

Preferably, the liquid can have an average density between 0.6 and 3.5 and an average viscosity between 0.1 and 1000 mPa.s.

The first back pressure applied during the second step can be between 5 and 800 mbar.

The vacuum applied during the fourth step can be between 5 and 200 mbar.

The second back pressure applied during the fifth step can be between 5 and 200 mbar.

Preferably, the first and second steps can be repeated 3 or 4 times when the rise in the liquid is less than or equal to 10 mm.

The permeable membrane used is preferably chosen from membranes of a cellulose nature conventionally made of cellulose acetate or of cellulose nitrate having cut-off thresholds of the order of 1 to 10 μm, or among the membranes composed of glass microfibers having similar cutoff thresholds.

The vacuum of the fourth step and the second back pressure of the fifth step are preferably applied respectively for durations varying from 60 seconds to 600 seconds.

The invention will now be described with the aid of the appended figures which in no way limit the subject of the invention. FIG. 1 is a schematic sectional view of the various elements constituting the apparatus intended to take the experimental measurements during the implementation of the method of the invention, - FIG. 2 represents the curve m = f (t) obtained with the five stages of the process according to example 1. figure 3 represents the different applications of back pressure and vacuum during the process according to example 1, figure 4 represents the curve m ² = f (t) necessary to obtain the value of the different slopes according to example 1.

As can be seen in FIG. 1, a glass reference tube 1 having an internal diameter of 8 mm, a section of 5.02610 ^"s m ² , and a total height which can vary from 30 to 120 mm is hermetically sealed. on its lower part 1a by a membrane 2, permeable to liquid and constituted by a filter paper.

The tube 1 is then filled to about 80% of its total height, with a finely divided solid 3 such as for example polytetrafluoroethylene (PTFE) or also with polyethylene. The solid can also consist of any chemical components of mineral or organic nature which can be put into a pulverulent state and which is insoluble in the probe liquid. The solid is packed mechanically and very carefully in the tube.

The lower part 1a of the tube 1 is then immersed in a liquid 4 placed in a cup 5. The liquid 4 is for example hexane, and has a density p of 660 kg / m2 and a viscosity η of 3.10 ^"4 Pa .s.

The cup 5 rests directly on a balance 6 having an accuracy ranging from 1/100 to 1/1000 g.

The balance 6 is also connected to a computer data processing system (not shown). During the first step, the liquid 4 rises freely by capillary action and in a known manner in the tube 1 through the permeable membrane 2 and the powder 3 up to 10 to 20% of its height of powder, so as to leave a portion of the powder not impregnated with the liquid 4.

Throughout the process of the invention, the evolution of the mass "m" of liquid 4 having risen in the tube 1 is measured continuously as a function of time "t". According to the mathematical equation m = f (t), the value of m is obtained by indirect weighing, because only the liquid 4 remaining in the dish 5 is weighed.

After this first step, we calculate the slope 1 of the curve (m ₁ ) ² = f (t ₁ ).

Then from the mathematical equation: 1 Ω _{expl =} slope 1 (equation IX)

OR P ² r ^L liq = η

the value of Ω _expl is obtained by calculation When the liquid 4 has reached 20% of the total height of the powder, a first vertical back pressure P _x directed from top to bottom is applied during the second step using d a syringe 7. The syringe 7 is filled with a gas, generally dry air or any other gas inert towards the liquid or the solid such as, for example, nitrogen, carbon dioxide, or more helium. The syringe 7 makes it possible to repel the liquid 4 partially mounted in the tube 1 in a regular and controlled manner. The syringe 7 makes it possible to apply an isostatic pressure P _x due to the direct presence of the "pushing" gas on the probe liquid 4. The syringe 7 is actuated using a movable actuator 7a. The syringe 7 is connected to the tube 1 by means of a pressure sensor 8, itself connected to a solenoid valve 9 for bringing it to atmospheric pressure, and it is connected to a seal 10 directly on the upper part 1b of the tube . When the system has stabilized, the back pressure P _x is equal to 209 mbar and the height of liquid 4 in the tube is 30.9 mm.

Knowing the liquid height, we deduce by calculation the value of εpgh from the mathematical equation (II):

ΔP = (A.Δγ) - (εpgh) Finally also knowing the pressure variation ΔP, we can calculate the value of (A.Δγ).

During the third step, we stop applying the first PI back pressure so as to leave again, freely mount the liquid 4 in the tube 1, and this time until all of the solid 3 is immersed in the liquid 4.

^' The continuous measurement of the variation in mass of liquid 4 in the tube as a function of time, gives a numerical value of this mass "m" at saturation, ie 0.9 grams.

By mathematical calculation, we get the value of slope 2. And by applying the mathematical equation again

(IV) (cited above) we obtain the value of Ω _exp2 , the value of the porosity ε and therefore the value of β

(tortuosity coefficient).

Then, during the fourth step, a vacuum P ₂ = 7404 Pa is applied using the syringe

7. This vacuum is kept constant for 500 seconds.

The measurement of the variation in mass of liquid 4 as a function of time is always carried out. At the end of this fourth step, and after mathematical calculation, the value of the specific surface is obtained using the Kozeny-Carman formula:

ΔP ε ³

A ² = x (equation V) δ.η.hv (1-ε) ²

Finally, during the fifth step, a second pressure is applied again P3 = 7590 Pa kept constant for 500 seconds to allow correct reading of the values of change in mass of liquid 4 as a function of time and then calculate the area again specific A as defined in step 4.

The experimental results, obtained according to the detailed description above, are collated below. after.

Example 1

- Liquid: Hexane - Powder: PTFE

- Liquid density: p = 660 kg / m ³

- Liquid viscosity: η = 3.10 ^"4 Pa.s

- Tube height: 67 mm

- Powder weight: 3.97 grams - Inner diameter of the tube: 8 mm

- Tube surface: 5.0265.10 ^"5 m ²

- Powder volume: 3.367.10 ^"6 m ³ Phase 1

Measure _» slope 1 = 7,853.15 ^{" 4}

^C ALCULATION. Ω _expl = 2.7041.10 ^"13 kg. M / s ²

Ph se?.

Measures . mass of liquid blocked by the first back pressure: 0.59 g, back pressure: 209 mbar

Calculation _# height of liquid: 30.9 mm

• (A.Δγ) = 20954

Phase 3.

Measurements _# mass of liquid after saturation: 0.9 g

_# slope 2: 8,24.10 ^"4

Calculation. _Q = x slope 2

2χr _liq

η or 'ex a = x slope 2 = 2.8393.10 ^"13 kg.m / s ^:

2p ² ε = 0.405 Phase 4

Slope 3 measurements: 5.63.10 ^"7 kg / s

_• depression: -7404 Pa

Calculation. flow rate: 8.5389.10- ¹⁰ m ³ / s. speed = 1.6988.10 ^"5 m / s. A = 916770 m ² / m ³

Phase 5

Measures _• slope 4: 3.63.10 ^"7 kg / s

_• pressure: 7590 Pa

Calculation. flow rate: 5.50.10 ^"10 m ³ / s

. speed = 1,090.10 ^"5 m / s. A = 1131291 m ² / m ³

Final results • β 31315797

• I \ .l mean = 1.3545.10 -11 n / a

• Average Δγ =, 0689.10 ^-2 mJ / m ²

• average γ _s ⁼ 20.8 mJ / m

Example 2:

- Liquid: Hexane

- Powder: polyethylene - Liquid density: p = 660 kg / m ³

- Liquid viscosity: η = 3.10 ^"4 Pa.s

- Tube height: h = 69 mm

- Powder weight: 1.64 grams

- Inner diameter of the tube: 8 mm - Powder volume: 3,468.10 ^"6 m ³

Phase 1 Measure. Slope 1 = 3.01.10 ^"3

Calculation. Ω _expl = 1,036.10- "kg.m / s ² Phase 2

Measurements, Mass of liquid blocked by the first back pressure: 0.32 g _• Back pressure: 7.45 mbar

Calculations _φ Height of liquid: 19.5 mm

(A.Δγ) = 808

Phas _3

Liquid mass measurements after saturation 1.13 g. slope 2: 3.30.10 ^"3

Calculations Ω, exp2 = l, 136.10 ^"12 kg. / S ε = 0.495

Phase 4

Measures _# slope 3: 2,4.10 ^-4 kg / s _# Depression: 1075 Pa

Calculations _# flow = 3.64.10 ^"7 m ³ / s. Speed = 0.0723 m ² / s. A = 26293 m ² / m ³

Phase 5

Measures _# slope 4: 2,4.10 ^'4 kg / s _" depression: 1014 Pa

Calculations. flow rate = 3.64.10 ^"7 m ³ / s. speed ≈ 0.0723 m ² / s. A = 25440 m ² / m ³

Resu 1-.a R fiπai.y

_# β = 461409

r medium _soil 3.47.1G- ¹¹

Average Δγ 3.13.10 ^"2 mJ / m ²

γ _s average 33.6 mJ / m ²

Claims

1. Method for determining the numerical value of the surface energy γ of a finely divided solid from different experimental measurements and from different mathematical equations consisting of:

- take a tube the lower end of which is hermetically sealed by a liquid-permeable membrane, - fill it to about 80% of its total volume with said divided solid,

- immersing the lower part closed by the membrane in a liquid,

- allow the liquid to rise freely during a first phase in the tube,

- to measure the mass of the liquid mounted in the tube as a function of time by monitoring the change in mass of the remaining liquid, in order to obtain the slope 1 of the straight line described by the following equation (I): m ² = f (t) (equation I) characterized in that it consists:

- in a second phase, when 10 to 20% of the total height of the powder is in contact with the liquid, a first back pressure is applied to the upper part of the capillary tube so as to stop the capillary rise of the liquid in the tube through the divided solid, and measures the numerical value of the mass of liquid remaining after rise of the liquid so as to deduce therefrom, after mathematical calculation, the mass of liquid mounted in the tube as soon as the assembly constituted by the pressure and the mass variation has stabilized, then after applying the mathematical equation: ΔP = (A.Δγ) - (εpgh) (Equation II) to obtain the numerical value of (A.Δγ)

- A is the specific area of the finely divided solid (m ² / m ³ ), - ΔY = γ _s - γ _S L is the difference between the surface energy of the solid (γ _s ) and the solid interfacial energy - liquid (γ _SL ),

- ε is the porosity of the solid,

- p is the density of the liquid, - g is the acceleration of gravity (9,81),

- h is at the height of the finely divided solid in the tube,

- ΔP is the pressure variation applied to the tube, - to stop, in a third phase, the application of the first counter pressure so as to allow the liquid to rise freely in the tube until the divided solid is completely submerged by the liquid present in the tube, and to measure regularly and continuously the variation of the mass of remaining liquid, after the rise of the liquid in the tube, as a function of time, to then deduce after mathematical calculation the total mass of the mounted liquid in the tube, and then obtain, after application of the mathematical equation (I), the slope 2, then the porosity ε according to the following equation (III):

volume of liquid at saturation _ε = (equation III) volume of powder in the tube

then by applying the mathematical equation (IV):

Ω _exp = (equation IV) β or

- Ω _exp (kg.m / s ² ) is equal to [1 / (2 xr _ιiq )] x slope 2 with r _ιiq = p / η, η being the viscosity of the probe liquid in Pa. S,

- R is the internal radius of the tube

- ε is the porosity of the solid divided the numerical value of β, where β is the coefficient of tortuosity, - to apply, in a fourth step, on the upper part of the tube a depression kept constant for a period ranging from approximately 300 to 1000 seconds so as to measure the numerical value of the liquid mass remaining after the liquid has risen in the tube, to then deduce therefrom by mathematical calculation the kinetics of variation of the mass of liquid mounted in the tube, then the numerical value of the specific area A (m ² / m ³ ) of the powder, contained in the tube from the following Kozeny-Carman equation (V):

.DELTA.P

_A 2 _ x Equation (V)

5.η.h.v (1-ε)

or

- ΔP is the pressure variation applied to the tube,

- η is the viscosity of the liquid, - h is the height of powder in the tube,

- v is the rate of ascent of the liquid,

- ε is the porosity of the divided solid, - And to apply again, in a fifth step, on the upper part of the tube, a second counter pressure kept constant for a period ranging from approximately 300 to 1000 seconds so as to calculate again the numerical value of the specific area A (m ² / m ³ ) as defined in step 4.

2. Method according to claim 1, characterized in that the divided solid is chosen from organic or inorganic polymers of synthetic origin such as for example polytetrafluoroethylene or polyethylene, or from organic or inorganic polymers of natural origin such as talc, glass, flour of various cereals or among the bacterial walls.

3. Method according to claim 1, characterized in that the liquid is chosen from alkanes such as pentane, hexaήe, heptane, octane, nonane, decane, cyclohexane, 1 'hexadecane, cis-decaline, 1 '-bromonaphthalene, diiodomethane, or among other organic compounds such as methanol, ethanol, methyl ethyl ketone, tetrahydrofuran, ethylene glycol, glycerol, formamide, dimethyl sulfide, the water.

4. Method according to one of claims 1 or 3, characterized in that the liquid has an average density between 0, 6 and 3.5 and an average viscosity between 0.1 and 1000 mPa.s.

5. Method according to claim 1, characterized in that the first counter pressure applied in the second step can be between 5 and 800 mbar.

6. Method according to claim 1, characterized in that the vacuum applied in the fourth step is' between 5 and 200 mbar.

7. Method according to claim 1, characterized in that the second back pressure applied in the fifth step is between 5 and 200 mbar.

8. Method according to claim 1, characterized in that the first and the second steps are repeated successively 3 or 4 times when the rise of the liquid is less than or equal to 10 mm.

9. Method according to claim 1, characterized in that the membrane is preferably chosen from membranes of cellulosic nature conventionally made of cellulose acetate or of cellulose nitrate having cutoff thresholds of the order of 1 to 10 μm, or still among the membranes composed of glass microfibers having similar cutoff thresholds.

10. Method according to claim 1, characterized in that the depression of the fourth step and the second back pressure of the fifth step are preferably respectively applied for durations varying from 60 to 600 seconds.

11. Use of the method as defined according to one of the preceding claims for determining the surface energy of finely divided solid entering into the chemical composition of solid-liquid dispersion of ink paints, adhesives, resins.

12 .. Use of the process as defined according to one of claims 1 to 10, for determining the surface energy of a finely divided, agglomerated solid.